Hi

I am having trouble on working out the following question:

Given C is the anticlockwise circular path $\displaystyle x^2+y^2=4$, starting and ending at (0,2) evaluate the line integrals $\displaystyle \oint_C F.dr$ where $\displaystyle F = xyi+xyj$

This is what i have done

$\displaystyle r=xi + yj$

$\displaystyle dr = i + j$

$\displaystyle x=2cos(\theta)$, $\displaystyle y=2sin(\theta)$

$\displaystyle F = (4cos(\theta) sin(\theta))i + (4cos\theta sin\theta )j$

$\displaystyle \int_{0}^(2\pi) (4cos\theta sin\theta)i + (4cos\theta sin\theta )j \cdot i + j$

P.S